Math Problem Statement

Given F(A, B, C, D) = Σm(4, 6, 7, 8, 12, 15) and d(A, B, C, D) = Σm(2, 3, 5, 10, 11, 14), identify the correct K-map from the provided options.

Solution

It seems you've uploaded two images. Based on the initial glimpse, these images involve Karnaugh maps (K-maps), which are used for simplifying Boolean functions. The provided Boolean functions are as follows:

  • F(A,B,C,D)=Σm(4,6,7,8,12,15)F(A, B, C, D) = \Sigma m(4, 6, 7, 8, 12, 15)
  • d(A,B,C,D)=Σm(2,3,5,10,11,14)d(A, B, C, D) = \Sigma m(2, 3, 5, 10, 11, 14)

These expressions represent the minterms for the function FF and the don't-care conditions for dd.

The K-maps have 16 cells representing all possible combinations of the variables AA, BB, CC, and DD. The numbers in parentheses correspond to the binary indices of the minterms.

Let me help you analyze the K-maps step by step:

  1. Minterms for F: We need to map the minterms (4, 6, 7, 8, 12, 15) to the K-map and place 1's in the respective cells.
  2. Don't-Care Conditions: We also need to mark the don't-care conditions (2, 3, 5, 10, 11, 14) as 'X' (don't care).
  3. Choosing the Correct K-map: We'll then check which K-map correctly represents this arrangement.

Let me start by analyzing these details based on the uploaded images.It seems like I can’t do more advanced data analysis right now. Please try again later. However, I can still help guide you through the solution manually.

If you want, I can explain how to map the minterms and don't-care conditions to the K-map and identify the correct option. Would you like me to proceed with that?

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Math Problem Analysis

Mathematical Concepts

Boolean Algebra
Karnaugh Maps
Simplification of Boolean Functions

Formulas

Minterms and Maxterms
K-map groupings for simplification

Theorems

Boolean simplification rules
Consensus theorem
Distributive and Absorption Laws

Suitable Grade Level

Grades 10-12